{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "n=10000\n",
    "m=10\n",
    "p=3 #Barabasi-Albert parameter\n",
    "init_Theta=0.05#0.06\n",
    "N=10 #number of time steps\n",
    "r=0 #0.3 #szansa aktywacji przy negatywnej korelacji\n",
    "prob=0.20 #prawd. aktywności użytkownika w danej epidemii (do generaowania macierzy)\n",
    "a=0.15#0.04 # parameter kształtu powr-law"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.Undirected graph done!\n",
      "2.Directed graph done!\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "04fb3892c36f489a8e9d6858f615bbdd",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>HBox</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=59982), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "3.Wieghts assigned!\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "cabc2b9c34134dff8dd9c09e9d790134",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>HBox</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=10000), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "4.Wieghts normalized!\n",
      "4.Adjacency (sparse) matrix created!\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import copy\n",
    "import math\n",
    "import pandas as pd\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "np.set_printoptions(threshold=np.nan)\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm import tqdm_notebook as tqdm\n",
    "import networkx as nx\n",
    "import scipy.sparse as sparse\n",
    "import asizeof\n",
    "from collections import defaultdict\n",
    "G=nx.barabasi_albert_graph(n, p)\n",
    "print('1.Undirected graph done!')\n",
    "G=G.to_directed()\n",
    "print('2.Directed graph done!')\n",
    "for u,v in tqdm(G.edges()):\n",
    "    G[u][v]['weight']=1.0#np.random.uniform(0,1)\n",
    "print('3.Wieghts assigned!')\n",
    "for i in tqdm(range(n)):\n",
    "    in_degree=G.in_degree(i,weight='weight')\n",
    "    for u,v in G.in_edges(i):\n",
    "        #print(u,v,G[u][v]['weight'],G[u][v]['weight'] / in_degree, in_degree)\n",
    "        G[u][v]['weight']/=in_degree\n",
    "print('4.Wieghts normalized!')\n",
    "W=nx.adjacency_matrix(G,weight='weight')\n",
    "print('4.Adjacency (sparse) matrix created!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.994210761621 1.0 0.0202256085746 0.0550340548402\n",
      "Correlation matrix done!\n"
     ]
    }
   ],
   "source": [
    "C = np.random.random((m, m))\n",
    "C=C*2-1\n",
    "C *= np.tri(*C.shape,k=-1)\n",
    "C=C+np.transpose(C)+np.eye(m)\n",
    "print(C.min(),C.max(),C.mean(),np.median(C))\n",
    "print(\"Correlation matrix done!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ead2035615364eb0bf4fab9589c3641b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>HBox</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=10), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Initial state assigned!\n"
     ]
    }
   ],
   "source": [
    "indykatory=[]\n",
    "frakcje=[]\n",
    "import scipy.stats as stats\n",
    "frac_inf=np.ceil(stats.powerlaw.rvs(a,size=(m))*n).astype(int)\n",
    "I=np.full((n, m), False, dtype=bool)\n",
    "for i in tqdm(range(m)):\n",
    "    I[np.ix_(stats.randint.rvs(0, n-1, size=frac_inf[i]),[i])]=True\n",
    "indykatory.append(I)\n",
    "frakcje.append(np.vstack((range(m),np.sum(I,axis=0)/n)))\n",
    "I=copy.deepcopy(I)\n",
    "print(\"Initial state assigned!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial Theta assigned!\n"
     ]
    }
   ],
   "source": [
    "Theta=np.full((n,m), init_Theta)\n",
    "print(\"Initial Theta assigned!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Activation counter initiated!\n"
     ]
    }
   ],
   "source": [
    "Y=np.full((n,1),0)\n",
    "print(\"Activation counter initiated!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "dc9ad45b87fa4d92b10027423f48b9df",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>HBox</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=10), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "df=[]\n",
    "for l in tqdm(range(N)):    \n",
    "    U=W.transpose().dot(I)\n",
    "    F=U.dot(C)/m\n",
    "    #print(F.min(),F.max(),F.mean(),l)\n",
    "    temp=np.greater_equal(F, Theta) #porównanie funkcji aktywacji z progiem\n",
    "    ### dodawanie rekordów bez przekroczenia progu\n",
    "    for i in np.unique(np.where(temp[:,:]==False)[0]):\n",
    "        temp1=np.where(temp[i,:]==False)[0] #tagi, w których dla użytkownika i przekroczony nie był próg\n",
    "        temp2=np.where(I[i][:]==True)[0] #tagi juz aktywne\n",
    "        temp1=np.setdiff1d(temp1,temp2) #usuniecie juz aktywnych tagow\n",
    "        for j in temp1:\n",
    "            df.append([i,copy.deepcopy(F[i][j]),0,copy.deepcopy(Y[i][0])])\n",
    "    ###\n",
    "    for i in np.unique(np.where(temp[:,:]==True)[0]): #iteracja po użytkownikach, którzy mają przekroczony próg\n",
    "        temp1=np.where(temp[i,:]==True)[0] #tagi, w których dla użytkownika i przekroczony był próg\n",
    "        temp2=np.where(I[i][:]==True)[0] #tagi juz aktywne\n",
    "        temp1=np.setdiff1d(temp1,temp2) #usuniecie juz aktywnych tagow\n",
    "    ### dodawanie rekordów z przekroczeniem progów\n",
    "        for j in temp1:\n",
    "            df.append([i,copy.deepcopy(F[i][j]),1,copy.deepcopy(Y[i][0])])\n",
    "    ### \n",
    "        if (not np.any(C[temp1[:, None],temp1]<0)) and (not temp1.size==0): #sprawdzenie, czy kandydaci do aktywacji nie są negatywnie skorelowani\n",
    "            I[i][temp1]=True #aktywacja uzytkownika i w tagach z listy temp1\n",
    "            Y[i][0]+=1#Y[i]+=1 #zwiekszenie licznika aktywacji uzytkownika i\n",
    "            Theta[i]=1-math.pow(1-init_Theta,Y[i][0]+1) #aktualizacja thety\n",
    "        else:\n",
    "            if (np.random.rand()<r) and (not temp1.size==0): #aktywacji pomimo negatywnej korelacji z pr. r\n",
    "                I[i][temp1]=True\n",
    "                Y[i][0]+=1\n",
    "                Theta[i]=1-math.pow(1-init_Theta,Y[i][0]+1)\n",
    "                if temp1.size==0:\n",
    "                    print('empty!')\n",
    "    indykatory.append(I)\n",
    "    frakcje.append(np.vstack((range(m),np.sum(I,axis=0)/n)))\n",
    "    I=copy.deepcopy(I)\n",
    "del temp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a78b9e7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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yG3gj8KVuJ+nUR4E/Ap7vepANYA9wAvi7/mmqe5Ns63qoLlTVIvAR4BhLl0T5XlV9rtup\n1t9mi7vOI8l24NPA71fV/3Q9TxeS/DrwbFV1dT2bjWYSeBMwW1VvBE4BY/k9qiSvZOkV/h7gNcC2\nJL/d7VTrb7PF3cscrJJkC0thn6+qB7uep0NvBX4jyTdZOl33y0n+vtuROnUcOF5VL7yS+xRLsR9H\nvwJ8o6pOVNUZ4EHg5zqead1ttrgPcimEsZEkLJ1TfbKq/rrrebpUVX9cVTurajdLfy/+paqaPzq7\nkKr6L+DpJK/rL70deKLDkbp0DLguydb+18zbGYNvLl/Uq0K+XBe6FELHY3XprcB7gMeTfLW/9idV\n9XCHM2njeD8w3z8QOsL6XxZkQ6qqLyX5FPBllt5h9hXG4DIEXn5Akhq02U7LSJIGYNwlqUHGXZIa\nZNwlqUHGXZIaZNwlqUHGXZIa9H8Vznei3H3tiAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a25e43320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a25da8048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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wGvjr3sNU9yfZ1vVQXaiqU8CHgBMsviTKd6rqs91Otf6GLe66iCTbgU8Bv1NV/9P1PF1I\n8qvAc1XV1WuWbDbjwJuAmap6I3AWGMnnqJK8isX/4e8BXgdsS/Kb3U61/oYt7r7MwQpJtrAY9rmq\neqjreTr0FuDXkvwHiw/X/WKSv+l2pE6dBE5W1Xf/J/dJFmM/in4J+HpVna6q88BDwM90PNO6G7a4\n9/NSCCMjSVh8TPWpqvqLrufpUlX9QVXtrKrdLP67+Keqav7o7FKq6j+BZ5K8obf0NuDJDkfq0gng\nxiRbe18zb2MEnlze0FeFfKUu9VIIHY/VpbcA7waeSPKV3tofVtUjHc6kzeN9wFzvQOgY6/+yIJtS\nVX0xySeBL7F4htmXGYGXIfDlBySpQcP2sIwkqQ/GXZIaZNwlqUHGXZIaZNwlqUHGXZIaZNwlqUH/\nB7EAfqB4+u8gAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a25e68898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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lJB9N8iNdz7TRtlTcl0+FcA9wM7AfuC3J/m6n6tR54A+raj/wGuDtI35/ALwTeKLrITaJ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\nLkkNMu6S1KD/B5W5iDPVa2XPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a25db9b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a25bb7f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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o362qz3U71fIbtbjrApKsAz4N/E5V/W/X83Qhya8CT1dVV8ezWWkmgTcCe6vqDcCzwFi+\nR5XkZfT+hb8VeBWwNslvdjvV8hu1uHuYgwWSrKYX9tmqerDreTr0ZuDXkjxJ7+W6X0ryyW5H6tRx\n4HhVPf8vuQfoxX4c/TLwjao6WVVngAeBn+14pmU3anEf5FAIYyNJ6L2m+nhV/XXX83Spqv6gqjZW\n1RZ6fy7+uaqaf3Z2MVX1X8CxJK/tL70VeOwS/0vLjgI3JFnT/zvzVsbgzeXLelTIl+pih0LoeKwu\nvRl4F/Bokq/21/6wqh7qcCatHO8HZvtPhA6z/IcFWZGq6ktJHgC+TO8TZl9hDA5D4OEHJKlBo/ay\njCRpAMZdkhpk3CWpQcZdkhpk3CWpQcZdkhpk3CWpQf8PEQl71zYCDS4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a25ac7e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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33uJ+ro85GHlJJoA3A1/tdpJOfQz4Y+D5rgdZA3YCx4FP9U9T3Zlkc9dDdaGqjgF/DRyh\n95EoP6iqL3Y71epbb3HXWSTZAnwO+IOq+t+u5+lCkt8Anqqqrj7PZq0ZB94CzFTVm4FngJF8jSrJ\nK+n9C38n8Fpgc5Lf6Xaq1bfe4u7HHCyRZCO9sM9V1b1dz9OhtwG/meRxeqfrfjXJ33c7UqeOAker\n6oV/yd1DL/aj6NeAb1fV8ap6DrgX+IWOZ1p16y3ug3wUwshIEnrnVB+tqr/tep4uVdWfVNX2qpqg\n9+fiX6qq+Wdn51JV/wU8keQN/aV3AI+c539p2RHg6iSb+n9n3sEIvLh8QT8V8uU610chdDxWl94G\nvBd4OMk3+mt/WlX3dziT1o4PAHP9J0KHWf2PBVmTquqrSe4BvkbvJ8y+zgh8DIEfPyBJDVpvp2Uk\nSQMw7pLUIOMuSQ0y7pLUIOMuSQ0y7pLUIOMuSQ36f2vkgGYCgS+9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a25a8b2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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oLlTVCeCvgKP0Lony/ar6bLdTrby1FnedQ5KNwCeB36+q/+l6ni4k+XXgqaq6ZNdOWeXG\ngTcCe6vqDcAzwEi+RpXkFfT+h78deBWwIclvdzvVyltrcfcyB4skWU8v7LNV9UDX83TozcBvJHmS\n3uG6X07y8W5H6tRx4HhVvfA/ufvpxX4U/Qrwzao6WVXPAg8AP9fxTCturcV9kEshjIwkoXdM9fGq\n+puu5+lSVb2/qjZX1TZ6Xxf/UlXNPzs7n6r6T+BYktf2l94CPNbhSF06ClyTZKL/PfMWRuDF5Ut6\nVciX6nyXQuh4rC69GXgn8GiSr/bX/riqHuxwJq0e7wFm+0+EDrPylwVZlarqS0nuB75M7x1mX2EE\nLkPg5QckqUFr7bCMJGkAxl2SGmTcJalBxl2SGmTcJalBxl2SGmTcJalB/wfAvLLqmpMW8wAAAABJ\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a25ac7ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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12W6nWn+jFnedQZItwCeB36+q/+l6ni4k+XXgiao6b5+dssFNAm8EZqvqDcBTwFi+R5Xk\nFfT+h78beBVwYZLf7naq9TdqcfdjDpZJsple2Oer6p6u5+nQm4HfSPIYvZfrfjnJx7sdqVPHgeNV\n9fz/5O6mF/tx9CvAN6vqZFU9A9wD/FzHM627UYv7IB+FMDaShN5rqo9U1d90PU+Xqur9VbW9qnbR\ne1z8S1U1/+zsbKrqP4HHk7y2v/QW4OEOR+rSMeCKJFP975m3MAZvLp/XT4V8qc72UQgdj9WlNwPv\nBB5K8tX+2h9X1X0dzqSN4z3AfP+J0BHW/2NBNqSq+lKSu4Ev0zvC7CuMwccQ+PEDktSgUXtZRpI0\nAOMuSQ0y7pLUIOMuSQ0y7pLUIOMuSQ0y7pLUoP8DFMS7mVTDdIIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a25c08cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a25ba8cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(N+1):\n",
    "    plt.plot(frakcje[i][1], 'ro')\n",
    "    axes = plt.gca()\n",
    "    axes.set_ylim([0,1])\n",
    "    if i>0:\n",
    "        wzrost=frakcje[i][np.ix_([0,1],np.where(frakcje[i]>frakcje[i-1])[1])]\n",
    "        plt.plot(wzrost[0],wzrost[1], 'go')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(N):\n",
    "    if np.array_equal(indykatory[i],indykatory[i+1])==True:\n",
    "        print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "df=pd.DataFrame(df)\n",
    "df.columns=['user','x','y','w']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pandas import DataFrame\n",
    "from sklearn import preprocessing\n",
    "from numpy import loadtxt, where\n",
    "from pylab import scatter, show, legend, xlabel, ylabel\n",
    "\n",
    "##The sigmoid function adjusts the cost function hypotheses to adjust the algorithm proportionally for worse estimations\n",
    "def Sigmoid(z):\n",
    "    G_of_Z = float(1.0 / float((1.0 + math.exp(-1.0*z))))\n",
    "    return G_of_Z\n",
    "\n",
    "##The hypothesis is the linear combination of all the known factors x[i] and their current estimated coefficients theta[i] \n",
    "##This hypothesis will be used to calculate each instance of the Cost Function\n",
    "def Hypothesis(theta, x):\n",
    "    z = x-theta\n",
    "    return Sigmoid(z)\n",
    "\n",
    "##For each member of the dataset, the result (Y) determines which variation of the cost function is used\n",
    "##The Y = 0 cost function punishes high probability estimations, and the Y = 1 it punishes low scores\n",
    "##The \"punishment\" makes the change in the gradient of ThetaCurrent - Average(CostFunction(Dataset)) greater\n",
    "def Cost_Function(X,Y,theta,m):\n",
    "    sumOfErrors = 0\n",
    "    for i in range(m):\n",
    "        hi = Hypothesis(theta,X[i])\n",
    "        error=Y[i]*math.log(hi)+(1-Y[i])*math.log(1-hi)\n",
    "        sumOfErrors += error\n",
    "    const = -1/m\n",
    "    J = const * sumOfErrors\n",
    "    return J\n",
    "\n",
    "##This function creates the gradient component for each Theta value \n",
    "##The gradient is the partial derivative by Theta of the current value of theta minus \n",
    "##a \"learning speed factor aplha\" times the average of all the cost functions for that theta\n",
    "##For each Theta there is a cost function calculated for each member of the dataset\n",
    "def Cost_Function_Derivative(X,Y,theta,m,alpha):\n",
    "    sumErrors = 0\n",
    "    for i in range(m):\n",
    "        xi = X[i]\n",
    "        hi = Hypothesis(theta,xi)\n",
    "        error = -1.0*(hi - Y[i])\n",
    "        sumErrors += error\n",
    "    constant = float(alpha)/float(m)\n",
    "    J = constant * sumErrors\n",
    "    return J\n",
    "\n",
    "\n",
    "##For each theta, the partial differential \n",
    "##The gradient, or vector from the current point in Theta-space (each theta value is its own dimension) to the more accurate point, \n",
    "##is the vector with each dimensional component being the partial differential for each theta value\n",
    "def Gradient_Descent(X,Y,theta,m,alpha):\n",
    "    CFDerivative = Cost_Function_Derivative(X,Y,theta,m,alpha)\n",
    "    new_theta = theta-CFDerivative\n",
    "    return [new_theta, CFDerivative]\n",
    "\n",
    "##The high level function for the LR algorithm which, for a number of steps (num_iters) finds gradients which take \n",
    "##the Theta values (coefficients of known factors) from an estimation closer (new_theta) to their \"optimum estimation\" which is the\n",
    "##set of values best representing the system in a linear combination model\n",
    "def Logistic_Regression(X,Y,alpha,theta,num_iters):\n",
    "    m = len(Y)\n",
    "    cost=[Cost_Function(X,Y,theta,m)]\n",
    "    Theta=[theta]\n",
    "    gradient=[]\n",
    "    for x in range(num_iters):\n",
    "        GD = Gradient_Descent(X,Y,theta,m,alpha)\n",
    "        theta = GD[0]\n",
    "        gradient.append(GD[1])\n",
    "        cost.append(Cost_Function(X,Y,theta,m))\n",
    "        Theta.append(theta)\n",
    "        if abs(GD[1])<0.00001:\n",
    "            break\n",
    "        #if x % 100 == 0:\n",
    "            #here the cost function is used to present the final hypothesis of the model in the same form for each gradient-step iteration\n",
    "            #print(\"theta \", theta, \" at \",x,\"-th iteration\")\n",
    "            #print(\"cost is \", Cost_Function(X,Y,W,theta,m))\n",
    "    return [Theta,cost,gradient]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from joblib import Parallel, delayed\n",
    "import time\n",
    "def text_progessbar(seq, total=None):\n",
    "    step = 1\n",
    "    tick = time.time()\n",
    "    while True:\n",
    "        time_diff = time.time()-tick\n",
    "        avg_speed = time_diff/step\n",
    "        total_str = 'of %n' % total if total else ''\n",
    "        print('user', step, '%.2f' % time_diff, 'avg: %.2f iter/sec' % avg_speed, total_str)\n",
    "        step += 1\n",
    "        yield next(seq)\n",
    "all_bar_funcs = {\n",
    "    'txt': lambda args: lambda x: text_progessbar(x, **args),\n",
    "    'None': lambda args: iter,\n",
    "}\n",
    "def ParallelExecutor(use_bar='tqdm', **joblib_args):\n",
    "    def aprun(bar=use_bar, **tq_args):\n",
    "        def tmp(op_iter):\n",
    "            if str(bar) in all_bar_funcs.keys():\n",
    "                bar_func = all_bar_funcs[str(bar)](tq_args)\n",
    "            else:\n",
    "                raise ValueError(\"Value %s not supported as bar type\"%bar)\n",
    "            return Parallel(**joblib_args)(bar_func(op_iter))\n",
    "        return tmp\n",
    "    return aprun\n",
    "n_jobs=22\n",
    "aprun = ParallelExecutor(n_jobs=n_jobs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Estimate_theta(df,user,initial_theta,alpha,num_iters):\n",
    "    res=[]\n",
    "    for i in df[df['user']==user]['w'].unique():\n",
    "        X=df[(df['user']==user) & (df['w']==i)]\n",
    "        Y=X['y']\n",
    "        Y=np.array(Y)#.reshape(-1, 1)\n",
    "        #print('srednia z W to ',np.mean(W))\n",
    "        X=X['x']\n",
    "        X=np.array(X).reshape(-1, 1)\n",
    "        mini=X.min(axis=0)\n",
    "        maxi=X.max(axis=0)\n",
    "        X=((X - mini) / (maxi - mini))*2-1\n",
    "        initial_theta=1-math.pow(1-initial_theta,i+1)\n",
    "        #initial_theta=((initial_theta - mini) / (maxi - mini))*2-1\n",
    "        LR=Logistic_Regression(X,Y,alpha,initial_theta,num_iters)\n",
    "        LR[0]=[(x+1)/2*(maxi-mini)+mini for x in LR[0]]\n",
    "        #LR[0]=[0 if x>1 else x for x in LR[0]]\n",
    "        LR[0]=[1-math.pow(1-x,1/float(i+1)) for x in LR[0]]\n",
    "        res.append(LR)\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a25bce908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "i=1\n",
    "X=df[(df['user']==0) & (df['w']==i)]\n",
    "Y=X['y']\n",
    "Y=np.array(Y)#.reshape(-1, 1)\n",
    "#print('srednia z W to ',np.mean(W))\n",
    "X=X['x']\n",
    "X=np.array(X).reshape(-1, 1)\n",
    "mini=X.min(axis=0)\n",
    "maxi=X.max(axis=0)\n",
    "X=((X - mini) / (maxi - mini))*2-1\n",
    "m=len(Y)\n",
    "for j in np.arange(-0,0.4,0.002):\n",
    "    plt.plot(j,1-math.pow(1-Cost_Function(X,Y,((j - mini) / (maxi - mini))*2-1,m),1/float(i+1)),'bo')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "60ca418ae6ae416ea9ec60d3987e7d55",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>HBox</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=3), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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rltXuHKip42tPLqCqNsSsq/PI6Kpz9UWk9UQT/CXAkIjHg4Np0bQ5G1jv7mXu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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f89af876550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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W4X7JRN/Tqi9uC2zTTO3RVh5cvZ/LJw9Tv3YRCUphHe5DE/szMzuZFwLc7r5s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\nP8raTpM+4wamAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a5d360c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2Z1eXMr2ylKmVJUytGMnUyhKmVIxkZKH+CUj+0f/1ktVKimJcOGUsF04Ze2KZ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\nGldXwnUFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a25e99ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Zqay8sCDRTRER6TehwsTMcs3sJTPbE7xP6KbcCjPbbWZlZrY2Xn0zu87MtpjZ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\nmIiISGgKExERCU1hIiIioSlMREQktP8PQsEG4HMBC5YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f89d4be49b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RFkAJIcZUVTn3vrqW5TsP8Nj1Ezh3aK9ohyQiLYS6jGLMA3/+jD+t28vsaSO4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a25cbf6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Qc26hcy7HOZeTkpISok23z/yJ6eSXVLFt/+Eu3S7Ar17bQo+oKG67cFSXb1tE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\nXUQkgBTuIiIB9P8B0hAtVFOUf30AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f89ea35c588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f89c23d7588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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8CxGJc+EGxjpgoze9EbhtiDargCPOuUrnXA/wuNdvxP5mdhtwDNgbZo1hebXy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\nhESBISIiIVFgiIhISBQYIiISkv8PccHUKFtVrqYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f89c23e0b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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U0kBFh8q5+ekFLNq6l1/fMFLXKIhIvUUiGBYCQ81sYHDweAowq0abWcBtwdlJ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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f89e8ed1080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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O75/Egi1FHDhivXuOp6yymhtfXE5+cTnPXpdJ76Q2bpdkjDkBC/4GTO7fiWqP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\n+AiY6Af78QDw83qW9dv9cGp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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f89ea331be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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lrEYNd+dcn5ndDDwChICfOOc2mdlN3vtrgAeB9wI7gE7ghvErWURERpPURAnO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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f89e7f13ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JWX07xQtyY12KiEjMRRUYZpZnZk+a2YHgedB3VjNbb2b7zKzUzDYM197MFphZ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\n6Y7vvpAsyjUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a25e99a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "initial_theta = 0\n",
    "alpha = 0.05\n",
    "iterations = 3000\n",
    "user=1\n",
    "res=Estimate_theta(df,user,initial_theta,alpha,iterations)\n",
    "for i in tqdm(range(len(res))):\n",
    "    initial_Theta=init_Theta\n",
    "    #print(initial_theta)\n",
    "    fig=plt.figure()\n",
    "    plt.plot(res[i][0])\n",
    "    fig.suptitle(f'theta values (true theta {initial_Theta:6.5})')\n",
    "    plt.show()\n",
    "    fig=plt.figure()\n",
    "    plt.plot([np.abs(x - initial_Theta)/ initial_Theta for x in res[i][0]])\n",
    "    fig.suptitle('theta fitt')\n",
    "    plt.show()\n",
    "    fig=plt.figure()\n",
    "    plt.plot(res[i][1])\n",
    "    fig.suptitle('cost')\n",
    "    plt.show()\n",
    "    fig=plt.figure()\n",
    "    plt.plot(res[i][2])\n",
    "    fig.suptitle('gradient')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "user 1 0.00 avg: 0.00 iter/sec \n",
      "user 2 0.00 avg: 0.00 iter/sec \n",
      "user 3 0.01 avg: 0.00 iter/sec \n",
      "user 4 0.01 avg: 0.00 iter/sec \n",
      "user 5 0.01 avg: 0.00 iter/sec \n",
      "user 6 0.01 avg: 0.00 iter/sec \n",
      "user 7 0.01 avg: 0.00 iter/sec \n",
      "user 8 0.02 avg: 0.00 iter/sec \n",
      "user 9 0.02 avg: 0.00 iter/sec \n",
      "user 10 0.02 avg: 0.00 iter/sec \n",
      "user 11 0.02 avg: 0.00 iter/sec \n",
      "user 12 0.02 avg: 0.00 iter/sec \n",
      "user 13 0.03 avg: 0.00 iter/sec \n",
      "user 14 0.03 avg: 0.00 iter/sec \n",
      "user 15 0.03 avg: 0.00 iter/sec \n",
      "user 16 0.03 avg: 0.00 iter/sec \n",
      "user 17 0.03 avg: 0.00 iter/sec \n",
      "user 18 0.04 avg: 0.00 iter/sec \n",
      "user 19 0.04 avg: 0.00 iter/sec \n",
      "user 20 0.04 avg: 0.00 iter/sec \n",
      "user 21 0.04 avg: 0.00 iter/sec \n",
      "user 22 0.04 avg: 0.00 iter/sec \n",
      "user 23 0.04 avg: 0.00 iter/sec \n",
      "user 24 0.04 avg: 0.00 iter/sec \n",
      "user 25 0.05 avg: 0.00 iter/sec \n",
      "user 26 0.05 avg: 0.00 iter/sec \n",
      "user 27 0.05 avg: 0.00 iter/sec \n",
      "user 28 0.05 avg: 0.00 iter/sec \n",
      "user 29 0.05 avg: 0.00 iter/sec \n",
      "user 30 0.05 avg: 0.00 iter/sec \n",
      "user 31 0.05 avg: 0.00 iter/sec \n",
      "user 32 0.05 avg: 0.00 iter/sec \n",
      "user 33 0.05 avg: 0.00 iter/sec \n",
      "user 34 0.06 avg: 0.00 iter/sec \n",
      "user 35 0.06 avg: 0.00 iter/sec \n",
      "user 36 0.06 avg: 0.00 iter/sec \n",
      "user 37 0.06 avg: 0.00 iter/sec \n",
      "user 38 0.06 avg: 0.00 iter/sec \n",
      "user 39 0.06 avg: 0.00 iter/sec \n",
      "user 40 0.06 avg: 0.00 iter/sec \n",
      "user 41 0.06 avg: 0.00 iter/sec \n",
      "user 42 0.06 avg: 0.00 iter/sec \n",
      "user 43 0.06 avg: 0.00 iter/sec \n",
      "user 44 0.07 avg: 0.00 iter/sec \n",
      "user 45 8.35 avg: 0.19 iter/sec \n",
      "user 46 8.62 avg: 0.19 iter/sec \n",
      "user 47 8.93 avg: 0.19 iter/sec \n",
      "user 48 8.98 avg: 0.19 iter/sec \n",
      "user 49 9.04 avg: 0.18 iter/sec \n",
      "user 50 9.11 avg: 0.18 iter/sec \n",
      "user 51 9.27 avg: 0.18 iter/sec \n",
      "user 52 9.44 avg: 0.18 iter/sec \n",
      "user 53 9.81 avg: 0.19 iter/sec \n",
      "user 54 9.87 avg: 0.18 iter/sec \n",
      "user 55 9.95 avg: 0.18 iter/sec \n",
      "user 56 10.04 avg: 0.18 iter/sec \n",
      "user 57 10.12 avg: 0.18 iter/sec \n",
      "user 58 10.37 avg: 0.18 iter/sec \n",
      "user 59 10.44 avg: 0.18 iter/sec \n",
      "user 60 10.52 avg: 0.18 iter/sec \n",
      "user 61 10.65 avg: 0.17 iter/sec \n",
      "user 62 10.87 avg: 0.18 iter/sec \n",
      "user 63 10.95 avg: 0.17 iter/sec \n",
      "user 64 11.24 avg: 0.18 iter/sec \n",
      "user 65 11.37 avg: 0.17 iter/sec \n",
      "user 66 11.48 avg: 0.17 iter/sec \n",
      "user 67 16.34 avg: 0.24 iter/sec \n",
      "user 68 17.09 avg: 0.25 iter/sec \n",
      "user 69 18.01 avg: 0.26 iter/sec \n",
      "user 70 18.30 avg: 0.26 iter/sec \n",
      "user 71 18.44 avg: 0.26 iter/sec \n",
      "user 72 18.49 avg: 0.26 iter/sec \n",
      "user 73 18.63 avg: 0.26 iter/sec \n",
      "user 74 18.71 avg: 0.25 iter/sec \n",
      "user 75 18.78 avg: 0.25 iter/sec \n",
      "user 76 18.86 avg: 0.25 iter/sec \n",
      "user 77 18.91 avg: 0.25 iter/sec \n",
      "user 78 18.96 avg: 0.24 iter/sec \n",
      "user 79 19.16 avg: 0.24 iter/sec \n",
      "user 80 19.20 avg: 0.24 iter/sec \n",
      "user 81 19.32 avg: 0.24 iter/sec \n",
      "user 82 19.41 avg: 0.24 iter/sec \n",
      "user 83 19.90 avg: 0.24 iter/sec \n",
      "user 84 20.03 avg: 0.24 iter/sec \n",
      "user 85 20.16 avg: 0.24 iter/sec \n",
      "user 86 20.80 avg: 0.24 iter/sec \n",
      "user 87 20.95 avg: 0.24 iter/sec \n",
      "user 88 21.03 avg: 0.24 iter/sec \n",
      "user 89 25.47 avg: 0.29 iter/sec \n",
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j5Hv1q4zO3scmOYvTZlEjU9vChWB6e7UQp0r8zgWKWwcncGBdNSFcmADwRubR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\nCwsDmJhKLCwsLCy6CFZwW1hYWJQMVnBbWFhYlAxWcFtYWFi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       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>HBox</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
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       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=1000), HTML(value='')))"
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     "name": "stdout",
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     "text": [
      "\n"
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    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f89bd4569b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=1000\n",
    "initial_theta = np.random.random_sample(n)/10\n",
    "alpha = 0.01\n",
    "iterations = 3000\n",
    "colors=['b', 'g', 'r', 'c', 'm', 'y', 'k', 'w']\n",
    "results=aprun(bar='txt')(delayed(Estimate_theta)(df,i,initial_theta[i],alpha,iterations) for i in range(n))\n",
    "for i in tqdm(range(n)):\n",
    "    for j in range(len(results[i])):#range(1):\n",
    "        initial_Theta=init_Theta\n",
    "        plt.plot(i,np.abs(results[i][j][0][-1] - initial_Theta)/ initial_Theta,colors[j]+'o',ms=1)\n",
    "plt.show()\n",
    "for i in tqdm(range(n)):\n",
    "    mean_theta=[]\n",
    "    for j in range(len(results[i])):#range(1):\n",
    "        mean_theta.append(results[i][j][0][-1])\n",
    "    initial_Theta=init_Theta\n",
    "    plt.plot(i,np.abs(np.mean(mean_theta) - initial_Theta)/ initial_Theta,'bo',ms=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "210ec62d1f7e4efbb3b070e9ab7179f6",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>HBox</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=10000), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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kfg+qClwRYRXB0og1IYSaulVQZGIzfJEb1vPLtJ0Qy6FsEGqCOKqSfZFVFKL9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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f89c282f748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in tqdm(range(n)):\n",
    "    mean_theta=[]\n",
    "    for j in range(len(results[i])):#range(1):\n",
    "        mean_theta.append(results[i][j][0][-1])\n",
    "    initial_Theta=init_Theta\n",
    "    plt.plot(i,np.abs(np.mean(mean_theta) - initial_Theta)/ initial_Theta,'bo',ms=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialized empty Git repository in /home/jovyan/Prediction of Viral Memes/.git/\r\n"
     ]
    }
   ],
   "source": [
    "!git add CC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# def plot_results(results,user):\n",
    "#     for j in range(len(results[user])):#range(1):\n",
    "#         initial_Theta=init_Theta\n",
    "#         plt.plot(user,np.abs(results[user][j][0][-1] - initial_Theta)/ initial_Theta,colors[j]+'o',ms=1)\n",
    "# aprun(bar='txt')(delayed(plot_results)(results,i) for i in range(n))\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_theta = np.random.random_sample(1000)/10\n",
    "alpha = 0.05\n",
    "iterations = 100\n",
    "results=aprun(bar='txt')(delayed(Estimate_theta)(df,i,initial_theta[i],alpha,iterations) for i in range(1000))\n",
    "est_theta=[]\n",
    "cost=[]\n",
    "hist_theta=[]\n",
    "gradient=[]\n",
    "for i in range(1000):\n",
    "    est_theta.append(results[i][0][100])\n",
    "    hist_theta.append(results[i][0])\n",
    "    cost.append(results[i][1])\n",
    "    gradient.append(results[i][2])\n",
    "plt.plot([np.abs(x - init_Theta)/ init_Theta for x in est_theta],'bo')\n",
    "plt.show()\n",
    "plt.plot(np.mean(np.array(cost), axis=0))\n",
    "plt.show()\n",
    "dop_theta=[]\n",
    "for i in range(1000):\n",
    "    dop_theta.append([np.abs(x - init_Theta)/ init_Theta for x in hist_theta[i]])\n",
    "plt.plot(np.mean(np.array(dop_theta), axis=0))\n",
    "plt.show()\n",
    "for i in range(1000):\n",
    "    dop_theta[i]=[(x-min(dop_theta[i]))/(max(dop_theta[i])-min(dop_theta[i])) for x in dop_theta[i]]\n",
    "plt.plot(np.mean(np.array(dop_theta), axis=0))\n",
    "plt.show()\n",
    "plt.plot(np.mean(np.array(gradient), axis=0)[1:])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.hist(np.array(cost)[:,98])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Wykres masymalnego w / liczba aktywnych kampanii na koniec procesu dla wszystkich użytkowników"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "tmp=[]\n",
    "for i in tqdm(range(df['user'].max()+1)):\n",
    "    tmp.append(sum(indykatory[N][i,:])/Y[i])\n",
    "plt.plot(tmp,'bo')\n",
    "del tmp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Różnica pomiędzy liczbą aktywacji z indykatorów, a licznikiem aktywacji"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "tmp=[]\n",
    "for i in tqdm(range(n)):\n",
    "    tmp.append(sum(np.logical_xor(indykatory[N][i,:],indykatory[0][i,:]))-Y[i][0])\n",
    "    #if sum(np.logical_xor(indykatory[N][i,:],indykatory[0][i,:]))-Y[i][0]<0:\n",
    "     #   print(i)\n",
    "plt.hist(tmp)\n",
    "plt.show()\n",
    "plt.plot(tmp,'bo')\n",
    "plt.show()\n",
    "del tmp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
